In recent years, sound provision with emphasis on spatial perception has been of increasing interest. In particular, it is in many applications desirable to produce a highly directional and narrow audio beam. For example, in virtual surround sound systems where virtual rear or side sound sources are generated from physical sound transducers positioned to the front of the user, highly directional sound beams may be reflected off walls to the side or rear of the user thereby providing the perception of virtual sound sources at these reflection points.
However, such narrow and highly directional beams may be difficult to generate from traditional audio band loudspeakers. Accordingly, an alternative approach has been proposed based on radiation of ultrasound from ultra sound transducers. Such speakers are known as parametric speakers. Essentially, a parametric loudspeaker is a device which generates audible sound through the nonlinear demodulation of a high intensity ultrasonic carrier wave modulated by an audio signal. Parametric loudspeakers are attractive for sound reproduction because they possess exceedingly high directionality at audio frequencies.
Thus, parametric loudspeakers use ultrasound transducers that can provide a highly directive sound beam. In general, the directivity (narrowness) of a loudspeaker depends on the size of the loudspeaker compared to the wavelengths. Audible sound has wavelengths ranging from a few inches to several feet, and because these wavelengths are comparable to the size of most loudspeakers, sound generally propagates omni-directionally. However, for an ultrasound transducer, the wavelength is much smaller and accordingly it is possible to create a sound source that is much larger than the radiated wavelengths thereby resulting in the formation of a very narrow and highly directional beam.
Such a highly directional beam can e.g. be controlled much better and can e.g. accurately be directed towards a desired reflection point.
The ultrasonic signal driving the ultrasound transducer is generated by amplitude modulating an ultrasound carrier signal by an audio signal derived from the audio signal being rendered. This modulated signal is radiated from the sound transducer. The ultrasound signal is not directly perceivable by a human listener but the audio signal can automatically become audible without the need for any specific functionality, receiver or hearing device. In particular, any nonlinearity in the audio path from the transducer to the listener can act as a demodulator thereby recreating the audio signal. Such a non-linearity may occur automatically in the transmission path. In particular, the air as a transmission medium inherently exhibits a non-linear characteristic that results in the ultrasound becoming audible. Thus, the non-linear properties of the air itself can cause the audio demodulation from a high intensity ultrasound signal. In this way the ultrasonic signal may automatically be demodulated to provide the audio sound to the listener.
Examples and further description of the use of parametric loudspeakers for audio radiation may for example be found in the PhD thesis “Sound from Ultrasound: The Parametric Array as an Audible Sound Source” by F. Joseph Pompei, 2002, Massachusetts Institute of Technology.
It has been found that the nonlinear demodulation process by which sound is produced by a parametric loudspeaker unfortunately gives rise to severe nonlinear distortion of the audio signal. Several distortion reducing pre-processing schemes for parametric loudspeakers have been proposed but the efficacy of these schemes is related to compromises between efficiency, bandwidth and processing complexity.
The article “Possible exploitation of non-linear acoustic in underwater transmitting applications” by Berktay, 1965, J. Sound Vib., 2(4), pages 435-461 provides an analytical far field approximation indicating that the demodulated audio signal created by the parametric effect in air is proportional to the second derivative of the square of the modulation envelope E(t), i.e.:
      y    ⁡          (      t      )        =                    ∂        2                    ∂                  t          2                      ⁢                  (                              E            ⁡                          (              t              )                                2                )            .      
Conventional parametric loudspeaker systems use a simple Amplitude Modulation (AM) of the carrier signal, i.e. the transducer driving signal s(t)is typically given as:s(t)=E(t)sin(ωct),where ωc is the angular frequency of the carrier signal and E(t) is the envelope of the drive signal.
In order to compensate for the non-linear distortion caused by the in-air demodulation of the ultrasonic signal, it has been proposed to pre-compensate the audio signal x(t) that is to be rendered. Specifically, it has been proposed to pre-compensate the audio signal by generating the envelope signal as:E(t)=√{square root over (1+∫∫mx(t))},
This ideal modulation envelope is given by the inverse of the nonlinear demodulation operation and since the transmitted signal must be real, the only modulation envelopes that result in an audio signal with no distortion components follow such an approach.
However, rather than use standard Double SideBand (DSB) AM modulation, it has been proposed to use Single SideBand (SSB) modulation for modulating the ultrasound carrier in parametric loudspeaker systems.
The standard modulation scheme is known as Dual Side Band (DSB) AM modulation since the amplitude modulation of the carrier frequency produces two side bands, an Upper Side Band (USB) and a Lower Side Band (LSB). These sidebands are equal in bandwidth to the modulation envelope, and contain the modulation information, as indicated in FIG. 1 which illustrates the audio spectrum 101 of the drive signal, the carrier frequency 103 and the resulting DSB AM modulated signal 105.
Under ideal conditions, AM, in combination with the ideal square root envelope pre-compensation results in a theoretically distortion free audio signal after demodulation. There are, however, several practical problems. The square root operation introduces an infinite harmonic sequence and therefore requires high bandwidth of the signal processing and in principle results in a pre-compensated signal with infinite spectrum. Indeed, in order to completely suppress all distortion components, this pre-compensated signal must be fully reproduced. Real transducers and electrical circuits are inherently band limited, preventing full reproduction of the drive signal. The consequence is potentially high levels of distortion. To reduce distortion either the modulation depth can be reduced or the bandwidth of the transducer and driving electronics must be made as wide as possible.
Reducing the modulation depth reduces the efficiency of the sound reproduction, with only modest reductions in distortion. Increasing the bandwidth of the transducer and driving electronics requires highly specialized equipment, rapidly increasing hardware costs. Further there are additional limits placed on the maximum permissible bandwidth of the signal. If the bandwidth is too large, the LSB information can leak into the audible frequency range. Not only would these audible components be annoying, but the Sound Pressure Levels (SPL) may be enough to cause permanent harm to the auditory system. All audible components of the LSB must therefore be removed by a filtering operation. This requirement places a hard limit on the available bandwidth, and restricts the distortion performance of the device. Also, subjective effects, such as headaches, nausea, excessive tiredness and a sense of fullness of the ears are linked with exposure to high frequency audible sound, and high intensity ultrasound in the near audible range. LSB components near the audible range may induce these unwanted symptoms, and a device designed for use over extended periods should make additional provisions for this. This again requires truncation of the pre-processed signal, further reducing the effectiveness of the distortion reduction.
In order to address such issues, it has been proposed to use a Single SideBand (SSB) AM modulation scheme to modulate the ultrasonic carrier rather than the conventional DSB AM modulation. SSB modulation schemes remove either the LSB or USB through use of a second orthogonal carrier wave. Modulation using such orthogonal carriers is known as quadrature modulation and may be represented as the modulation in the complex domain. As illustrated in FIG. 2, SSB may be similar to DSB modulation except that only one of the sideband signals is generated, in the example the USB 201.
SSB modulation promises many advantages over DSB modulation. The removal of the lower sideband prevents modulation information from leaking into the audible frequency region, and there is no hard limit on the permissible bandwidth. As there are no signal components near the audible frequency range, the carrier frequency can be lowered, reducing the atmospheric absorption of the ultrasonic energy which boosts the efficiency of the audio signal generation. In addition, the approach may ensure that there is no high intensity ultrasound in the near audible range and may thus provide increased safety and reduced subjective effects. Transmitting one sideband can reduce the bandwidth requirements of the transducer and driving electronics resulting in simpler, cheaper hardware. Reducing bandwidth can also result in savings in terms of electrical power.
However, while SSB may provide many advantages compared to SSB when modulating ultrasound signals for parametric loudspeakers, there are also some associated disadvantages. In particular, pre-compensation approaches used for DSB cannot directly be used for SSB.
Conventional SSB systems use the following modulation schemes(t)=g(t)sin(ωct)+ĝ(t)cos(ωct),where s(t) is the transducer driving signal, g(t) is the modulation signal ĝ(t) is the Hilbert transformed modulation signal and ωc is the angular frequency of the carrier signal.
The envelope function of s(t) is given by|s(t)|=√{square root over (g2(t)+(ĝ(t))2)}{square root over (g2(t)+(ĝ(t))2)}.
To provide distortion free audio it is necessary to find a signal g(t) such that√{square root over (g2(t)+(ĝ(t))2)}{square root over (g2(t)+(ĝ(t))2)}=E(t)=√{square root over (1+∫∫mx(t))}
Thus, for a given audio signal x(t) it is necessary to solve this equation in order to find a function g(t) that can be used to modulate the ultrasonic signal such that the in-air demodulation of the radiated modulated ultrasound signal results in the original audio signal x(t).
However, due to the complex relationship expressed by the function, and the complex and non-linear nature of the Hilbert transform and the square-root function, this is very complicated. U.S. Pat. No. 6,584,205 and the article Lee, K., & Gan, W. “Bandwidth-efficient recursive pth-order equalization for correction based distortion in parametric loudspeakers”, 2006, IEEE Trans. Audio. Speech and Lang. Proc., 14(2), 706-710 propose the use of an iterative pre-processing to slowly converge to an optimum value of g(t).
The proposed approaches involve iteratively adjusting the modulation signal g(t) until the SSB envelope function approximates the ideal envelope E(t). However, while such an approach is effective at reducing distortion levels, the iterative method is very computationally demanding and introduces significant delay into the audio chain. This requires a very significant amount of processing to implement in real time making it very costly. Indeed, U.S. Pat. No. 6,584,205 suggests that at least 8 iterations are needed for reasonable audio quality. The high processing power demanded by such an approach tends to make real time implementations very costly or impractical.
Although slightly different modulation approaches have been proposed, such as using e.g.:s(t)=(1+g(t))sin(ωct)+ĝ(t)cos(ωct)these approaches tend to suffer from the exact same problems.
It has been proposed to use simple relationships for determining the modulating function, such as e.g. g(t)=E(t) . However, such simplifications tend to provide poor pre-compensation and thus result in high levels of distortion and low audio quality.
Hence, an improved approach would be advantageous and in particular an approach allowing increased flexibility, reduced complexity, facilitated implementation, reduced computational resource compensation, improved pre-compensation, improved audio quality and/or improved performance would be advantageous.